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Computers in Human Behavior 59 (2016) 115e133

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Computers in Human Behavior

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Qualitative spatial reasoning methodology to determine the particulardomain of a set of geographic objects

Miguel Torres a, Eduardo Loza a, Wadee Al-Halabi b, *, Giovanni Guzman a,Rolando Quintero a, Marco Moreno-Ibarra a

a Instituto Polit�ecnico Nacional, CIC, Mexico UPALM-Zacatenco, 07320 Mexico City, Mexicob Computer Science Department, King Abdulaziz University, Jeddah, Saudi Arabia

a r t i c l e i n f o

Article history:Received 29 September 2015Received in revised form22 January 2016Accepted 24 January 2016Available online 8 February 2016

Keywords:Qualitative spatial reasoningConceptual frameworkApplication ontologySemantic descriptionInference

* Corresponding author.E-mail addresses: [email protected] (M. Torre

(E. Loza), [email protected] (W. Al-Ha(G. Guzman), [email protected] (R. Quintero(M. Moreno-Ibarra).

http://dx.doi.org/10.1016/j.chb.2016.01.0340747-5632/© 2016 Elsevier Ltd. All rights reserved.

a b s t r a c t

Nowadays, there are many geospatial information from different sources such as satellite images, aerialphotographs, maps, databases and others. They provide a comprehensive description of geographicobjects. However, the task to identify the geographic domain is not an easy task, because it involves asemantic processing related to inference approaches that are based on the conceptualization of a domain.These approaches allow us to understand in a similar way that human beings recognize the geographicentities and help us to avoid vagueness and uncertainty. In this paper, a methodology to perform aqualitative spatial reasoning in geospatial representations is proposed. It is based on a priori knowledge,which is explicitly formalized by means of an application ontology. The knowledge described in theontology is assessed according to a set of labels, belonging to any geographical domain for semanticanalysis and mapping those labels to matching concepts defined in the ontology. As result, a set ofgeographic domains ordered by their relevance is obtained, providing a general concept directly relatedto the input labels, simulating the way that we perceive cognitively any geographic domain in the realworld.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Reasoning about spatial data is a key task in many applications,including geographic information systems (GIS), meteorologicaland fluid-flow analysis, computer-aided design, and proteinstructure databases (Guesgen, Ligozat, Renz, & Rodríguez, 2008).Such applications often require the identification andmanipulationof qualitative spatial representations, for example, to detectwhether one object will soon occlude another in a digital image ordetermine efficiently relationships between a proposed road andwetland regions in a geographic data set. Qualitative spatialreasoning (QSR) provides representational primitives (spatial “vo-cabulary”) and inference mechanisms for these tasks (Bailey-Kellogg & Zhao, 2003). QSR has two primary goals: providing asymbolic model for human common-sense level of reasoning and

s), [email protected]), [email protected]), [email protected]

providing efficient means for reasoning (Wolter & Lee, 2010).The ability to perceive spatial objects and to reason about their

relationships seems effortless for humans but it has proved thatthese actions are so difficult for computers. They have alreadyattained the capabilities of a five-year-old child. Part of thecomputational problem lies in the difficulty of identifying andmanipulating qualitative spatial representations. For example,although the pixels in a digital image define the locations of spatialobjects implicitly, the task at hand might require a more qualitativecharacterization of the configuration of these objects, whether oneobject will soon occlude another (Bailey-Kellogg & Zhao, 1999).

Up-to-date GIS are becoming increasingly popular methods forrepresenting and reasoning with geographical data (Elmes et al.,2005; Goodchild, 2009). These applications require methods oflogical reasoning about geographical features and the relationshipsthat hold between them, including spatially (Hobbs, Blythe,Chalupsky, & Russ, 2006; Lei, Kao, Lin, & Sun, 2009). Thereasoning algorithms are widely used in the Artificial Intelligencefield, whose the most relevant tasks are the capability of verifyingthe consistency of data sets, updating the shared knowledge,deriving new knowledge and finding a minimal representation

M. Torres et al. / Computers in Human Behavior 59 (2016) 115e133116

(Donnelly, Bittner, & Rosse, 2006; Hernandez, 1994).However, before performing any reasoning task, it is necessary

to take into account a formal representation that allows us toconceptualize the domain knowledge of our interest (Renz, 2002;Buder & Schwind, 2012). In this case, ontologies are powerfultools to conceptualize any context, describing its concepts andexpressing its relationships (Zhou, Ding, & Finin, 2011). Ontologieshave also been cited as a method to carry out this reasoning (Mark,2003; Egenhofer & Mark, 1995), but there are methodologies thatdo not handle the inherent vagueness adequately (Sharma, 1996).In fact, features are often dependent on the context in which theyare made, with local knowledge affecting the definitions (Smith,1996).

Geographic entities are not often a clearly demarcated entity,because they are part of another object (Liu & Daneshmend, 2004).Therefore, the individualization of entities is more important withrespect to the geographic domains that they can belong orrepresent.

According to Bennett (2002), vagueness is inherent to thegeographical domain, with many features being context depen-dent, as well as lacking precise definitions and boundaries.Vagueness is not a defect of our communication language butrather a useful and integral part. As a consequence, GIS cannothandle multiple possible interpretations in a correct manner,whereby the lack of this feature implies the creation of new tech-niques that allow the handling of various meanings, one of these isthe inference based on reasoning.

Even though GISs are now a commonplace, the major problem isthat of interaction. With gigabytes of information stored either invector or raster format, present-day GISs do not sufficiently supportintuitive or common-sense oriented humanecomputer interaction.Users may wish to abstract away from the mass of numerical dataand specify a query in a way, which is essentially or at least largely,qualitative (Cohn & Renz, 2008). Arguably, the next generation GISwill be built on concepts arising from Naïve Geography (Egenhofer& Mark, 1995). Much of naïve geography should employ qualita-tive reasoning techniques, perhaps combined with the provision of“spatial query by sketch” (Egenhofer, 1997).

Qualitative reasoning is (QR) concerned not only with capturingthe everyday common-sense knowledge of the physical world, butalso the myriad equations used by engineers and scientists toexplain complex physical phenomenon, while creating quantitativemodels (Weld& Kleer,1989). Themain goal of qualitative reasoningis to make this knowledge explicit, so that given appropriatereasoning techniques, a machine could make predictions, di-agnostics and explanations of the behavior of physical systems in aqualitative manner, without recourse to an often intractable orperhaps unavailable quantitative model. According to that, notethat although one use for qualitative reasoning is that it allowsinferences to be made in absence of complete knowledge. It makesthis not by probabilistic or fuzzy techniques, which may rely onarbitrarily assigned probabilities or membership values, but also byrefusing to differentiate between quantities unless there is suffi-cient evidence to do so (Cohn & Hazarika, 2001).

The essence of QR is to find ways to represent continuousproperties of the world by discrete systems of symbols. One canalways quantize something continuously, but not all quantizationsare equally useful. One-way to state the idea is the relevanceprinciple: the distinctions made by a quantization must be relevantto the kind of reasoning performed (Forbus, 1984). The resulting setof qualitative values is termed a quantity space, in which indistin-guishable values have been identified into an equivalence class.There is normally a natural ordering (either partial or total) asso-ciated with a quantity space, and one form of simple but effectiveinference is to exploit the transitivity of the ordering relationship.

Another is to devise qualitative arithmetic algebras (Wolter &Zakharyaschev, 2000), typically these may produce ambiguousanswers. Much research in the qualitative reasoning literature isdevoted to overcoming the detrimental effects on the search spaceresulting from this ambiguity.

On the other hand, spatial reasoning in our everyday interactionwith the physical world, in most cases is driven by qualitative ab-stractions rather than complete a priori quantitative knowledge.Therefore, QR holds promise for developing theories for reasoningabout space. This justifies the increasing interest in the study ofspatial concepts from a cognitive point of view, which provoked thebirth of qualitative spatial reasoning within Artificial Intelligenceand also GIS (Cohn, Bennett, Gooday, & Gotts, 1997).

Research in QSR is motivated by a wide variety of possible ap-plications areas including GIS, robotic navigation, high level vision,spatial propositional semantics of natural languages, engineeringdesign, common-sense reasoning about physical systems andspecifying visual language syntax and semantics. There are otherapplication areas including qualitative document-structure recog-nition (El-Geresy & Abdelmoty, 2006), applications in biology(Schlieder, 1996) and domains where space is used as a metaphor(Bennett, 1996; Knauff, Strube, Jola, Rauh, & Schlieder, 2004).

The goal of answering qualitative queries addresses an impor-tant aspect of common-sense reasoning by human beings and it canbe found in many practical applications such as computer-aidedtutoring or diagram understanding. Because of the lack ofdetailed numeric information, representations used by the ap-proaches to data-poor problems are often carefully designed byhand with respect to an automatic task (Rauh et al., 2005).

In this work, we propose amethodology to perform a qualitativespatial reasoning, over a set of geospatial objects that are repre-sented as input labels and belongs to a certain geographic domain.Three algorithms that perform the spatial reasoning and theinference tasks are proposed. They use the knowledge explicitlydefined into application ontology and conceptual frameworks. Thereasoning process is fundamentally based on the compute of to-pological relationships, which are used to describe the behavior of ageospatial object and their interaction with others.

The paper is organized as follows: Section 2 presents the state ofthe art related to the work in this field. Section 3 describes theproposed methodology to perform the qualitative spatialreasoning. Section 4 depicts the experimental results, applying thereasoning algorithms. The conclusion and futureworks are outlinedin Section 5.

2. Related work

Spatial reasoning is an important issue in many applicationdomains and it has been presented since the theory of points andlines geometry, which is considered one of the oldest branched ofspatial reasoning (Renz, 2002). Other works on qualitative spatialreasoning are preceded by proposals oriented to spatial represen-tations, in which the goal is that they can be read and understoodby a machine (Sharma, 1996). In (Freksa, 1992) the importance of acorrect representation of the reality to perform an efficient spatialreasoning process is described. In this case, machines are used torepresent knowledge in a formal approach. However, the capturedinformation must contain descriptions as close to how the humanbeings perceive their environment (Egenhofer &Mark, 1995). Thus,one of the main objectives of qualitative spatial reasoning is to findappropriate methods to represent continuous properties in theworld, using a discrete symbols-based system (Cohn et al., 1997;Cohn & Hazarika, 2001).

According to the basis of QSR, in (Mark & Frank, 1991) somecognitive aspects of perception and knowledge representations as

M. Torres et al. / Computers in Human Behavior 59 (2016) 115e133 117

well as the explanation why spatial knowledge is of a particularinterest for cognitive science are explored. It is suggested that“spatial inference engines” provide the basis for rather generalcognitive capabilities inside and outside the spatial domain. Therole of abstraction in spatial reasoning and the advantages ofqualitative spatial knowledge over quantitative knowledge arediscussed. Thus, in (El-Geresy & Abdelmoty, 2004) a general qual-itative spatial reasoning engine (SPARQS) is proposed. Qualitativetreatment of information in large spatial databases is used tocomplement the quantitative approaches tomanage those systems;in particular, it is used for the automatic derivation of implicitspatial relationships and in maintaining the integrity of the data-base. To be of practical use, composition tables of spatial relation-ships between different types of objects need to be developed andintegrated in those systems. Examples of the application of themethod using different objects and different types of spatial re-lationships are presented and new composition tables are builtusing the reasoning engine. Issues related to computerehumaninteraction (CHI) integrating qualitative spatial reasoning into GISare proposed. In (Schultz, Guesgen, & Amor, 2006) three CHIchallenges when combining qualitative and quantitative methodsare addressed. (1) Manage the subjective, ambiguous nature ofqualitative terms, (2) Provide a powerful, yet simple query system,and (3) effectively visualizing a complex, fuzzy qualitative querysolution. A qualitative GIS called TreeSap is presented, whichdemonstrates that, with the use of CHI principles, query tools canbe both powerful and accessible to non-expert users.

In (Randell, Cui, & Cohn, 1992), a study about the evolution ofqualitative spatial representations is presented. Authors proposed aset of binary relations C(x,y). For instance, according to the demon-stration, the relationship “x connects y” is defined as symmetric andreflexive relationship. These kinds of relationships have beendefinedtoworkwith spatial regions, where vagueness can bemore commonamonggeographicentities.Otherproposals focusedon incorporatingqualitative spatial reasoning into GIS have been developed (Bennett,Cohn, & Isli, 1997). In this work, a logical approach based on formallogical representations and reasoning algorithms for manipulatingqualitative spatial information is defined.

In (Wallgrün, 2010), the qualitative spatial reasoning methods

Fig. 1. General framework of

for learning the topological map of an unknown environment aredescribed. The proposal consists of developing a topological map-ping framework that achieves robustness against ambiguity in theavailable information by tracking all possible graph hypothesessimultaneously. They exploit spatial reasoning to reduce the spaceof possible hypotheses. The considered constraints are qualitativedirection information and the assumption that the map is planar.The effects of absolute and relative direction information using twodifferent spatial calculi and combine the approach with a realmapping system based on Voronoi graphs are investigated.

Spatial reasoning has been applied to topographical data with agrounded geographical ontology (Mallenby & Bennett, 2007). Themethod consists of handling the vagueness in the domain moreeffectively. It uses methods of reasoning about the spatial relationsbetween regions within the data in order to use knowledge aboutregions defined in an ontology and allow reducing the computationof points location in the spatial relationships. In (Wang, Liu, Wang,& Liu, 2006), the conception and implementation of a tool based onspatial reasoning and spatial data mining (SRSDM) is presented. Inthis work a new spatial knowledge representation that integratestopology, direction, distance and size relations is proposed. SRSDMincludes the following features: extracting spatial relations,frameworks for traditional or new data mining algorithms. As acase study, SRSDM has been tested with agricultural data.

On the other hand, the problem to understand the semanticsbased on spatial reasoning about oriented straight-line segments ispresented in (Moratz, Lücke, & Mossakowski, 2011). According tothe problem, it is difficult to establish a sound constraint calculusbased on these relations. In this work, authors present the results ofa new investigation into dipole constraint calculi, which usesalgebraic methods to derive sound results about the composition ofrelations of dipole calculi. The method is denominated condensedsemantics, and it is an abstract symbolic model of a specific frag-ment of our domain. It is based on the fact that qualitative dipolerelations are invariant under orientation preserving affine trans-formations. The dipole calculi allows for a straightforward repre-sentation of prototypical reasoning tasks for spatial agents. In thesame context, in (Wolter & Lee, 2010) an approach to qualitativelyprocess directional relations, based on constraints that represents

the RAIN methodology.

1 Kaab means Earth in Mayan language.


positions in the plane is described.Problems associated with the integration of data between

incongruent boundary systems are outlined in (Eagleson, Escobar,& Williamson, 2003). The majority of spatial boundaries aredesigned in an uncoordinated manner with individual organiza-tions, generating individual boundaries to meet individual needs.As a result, current technologies for analyzing geospatial informa-tion, such as GISs, are not reaching their full potential. In responseto the problem of uncoordinated boundaries, the authors presentan algorithm for the hierarchical structuring of administrativeboundaries. This algorithm applies hierarchical spatial reasoningtheory to the automated structuring of polygons. In turn, thesestructured boundary systems facilitate accurate data integrationand analysis whilst meeting the spatial requirements of selectedagencies. Moreover, the formalization and reasoning about spatialsemantic integrity constraints is presented in (Bravo & Rodriguez,2012). The paper presents a formalization of spatial semanticintegrity constraints that provides a uniform specification of con-straints used in practice, which is fundamental to assess the dataquality of spatial databases. The formalization extends traditionalnotions of functional and inclusion dependencies to considerspatial attributes. This enables to impose topological relations be-tween spatial attributes and constraints on numerical attributesthat depend on spatial attributes. In (Grütter, Bauer-Messmer, &H€ageli, 2008), two approaches to represent the Region ConnectionCalculus (RCC) method in OWL-DL are described. The approachesare used to infer the relationships between all connecting spatialregions in any of the different RCC species using a complete cal-culus. The application is focused on searching spatial objects usingan ontology.

In similar application context, the qualitative spatial reasoninghas been used for high-resolution remote sensing image analysis(Brennan& Sowmya, 1998). In (Inglada&Michel, 2009), the RegionConnection Calculus technique is used for the analysis of satelliteimagery in order to fully exploit the richness of this kind of images.The processing consists of detecting complex objects and studyingthe relationships between the elementary objects that composethem. A graph-based representation of the spatial relationshipsbetween the regions of an image is used within a graph-matchingprocedure in order to implement an object detection algorithm.

In robotic navigation and computer vision fields, there areproposals for manipulation planning using qualitative spatialreasoning. In (Westphal, Dornhege, W€olfl, Gissler, & Nebel, 2011),an approach to generate heuristics for the probabilistic samplingstrategy from spatial plans that abstract from concrete metric datais presented. These spatial plans describe a free trajectory in theworkspace of the robot on a purely qualitative level, i.e., byemploying spatial relations from formalisms considered in thedomain of qualitative spatial and temporal reasoning. A discussionof such formalisms and constraint-based reasoning methods isoutlined. These formalisms can be applied to approximategeometrically feasible motions.

3. RAIN methodology

RAIN is a methodology that consists of establishing a set ofapproaches to perform a qualitative spatial reasoning task in se-mantic descriptions of the geographic context, taking into accounta priori knowledge of the geospatial domain. Thus, this knowledgeis formalized by means of an application ontology, so that it can bereadable by a machine.

RAIN is focused on the conceptualization of the concepts andrelationships involved in a given domain. It is proposed to answer aquestion about which domain belongs to a set of semantic de-scriptions and what is the relevance of the concepts in that domain.

RAIN allows us to know the domain or context of a set of semanticdescriptions that could appear disjointed. The methodology iscomposed of two stages: 1) Analysis and conceptualization and 2)Inference. In the first stage, we obtain the a priori knowledge, whichis defined according to the reasoning requirements. In the secondstage, a set of ordered domains, considering the proximity orsimilarity of the input descriptions is obtained. The generalframework of the RAIN methodology is shown in Fig. 1.

3.1. The analysis and conceptualization stage

The conceptualization task is based on GEONTO-MET approach(Torres, Quintero, Moreno-Ibarra, Menchaca-Mendez, & Guzman,2011), which is a methodology to build geographic domain ontol-ogies. In Fig. 2, the conceptualization process is depicted.

By considering GEONTO-MET, two sets of axiomatic relationsA1¼{is,has,does} and A2¼{prepositions} are used, in order todirectly translate the relationships between concepts, as a part ofthe conceptualization. In other words, the aim is to reduce theaxiomatic relationships in the ontology. For instance, topologicalrelations such as connect, contain, meet and among others aredefined as relational concepts in the conceptualization, whereuponmore expressivity, granularity and semantic richness in the repre-sentation are obtained (Torres et al., 2011).

3.1.1. The abstraction processThis process is in charged of making an exhaustive revision over

geographic objects that are involved in the set of geographic do-mains, in order to carry out an abstraction that defines a prioriknowledge. Information of the domains has been gatheredfrom Kaab-Ontology,1 defined in (Torres et al., 2011). The advantageof this ontology domain is that we can find abstract entities andtheir relationships. In addition, definitions of the dictionary ofNational Institute of Statistics, Geography and Informaticsof Mexico (INEGI) (INEGI, 1996) and National Center of BiomedicalOntologies (NCBO) are used. The result of the process is to obtainthe essential information of geographic objects and domains thatare of interest for the reasoning. In Fig. 3, a fragment of the pro-posed ontology, using Kaab-Ontology is depicted.

3.1.2. The synthesis processThis process receives the objects and domains from the

abstraction task, which will be used in the reasoning stage. It isimportant to point out that information is not structured yet;therefore, it is necessary to define each domain according to itsobject interaction or relationship involved in the domain. Thus, atopological relation is defined between the geographic objects. Ahierarchical relation described among them, considering theirproperties and synonyms in souch domains as well as in geographicobjects, represented in this relationship.

In this process a mapping of the geographic objects is carriedout, with respect to the defined concepts in the applicationontology. The mapping is performed for starting the population ofthe ontology with instances.

Kaab-Ontology contains a set of abstract entities of thegeographic domain, which aids to delimitate the domain andrestrict the number of concepts that are involved in each one. Fig. 4shows the synthesis process, where we can appreciate that the setof concepts and topological relations allow the definition of do-mains set, in which the domains interact with the ontology toextract the instances that will generalize the process. In otherwords, from the description of many specialized concepts, a general

Fig. 2. Tasks of the conceptualization process.

Fig. 3. Fragment of the RAIN ontology.


concept is obtained, which describes in a global form the conceptsin a given domain.

Moreover, in Fig. 5 the mapping approach related to linkinstances with Kaab and RAIN ontologies is presented.

3.1.3. The semantic assessment processThe semantic assessment process uses the ontology and a set of

tables for obtaining information with respect to concepts defini-tion, their relationships with other concepts as well as their do-mains, rules and constraints. The goal of this task is to refine andassign a semantic value to each domain, taking into account theconstruction of concepts tables, which are composed of the prop-erties, location in the hierarchy, names and synonyms, as well as asynonyms concepts table, a domains table, a synonyms domainstable, a frequency table of concepts in the domains, a compositiontable of ordered topological relations according to their relevance,and finally a semantic refinement table in order to improve theinference method based on the feedback. These tables are definedas follows.

3.1.3.1. The concepts table. In this table, all the possible conceptsthat are part of each domain are shown. It allows us to explicitlyexpress the characteristics that each concept contains. The tablehas information about the synonyms such as concepts and prop-erties that are generally known. Additionally, the location of eachconcept in the hierarchy is known, identifying the concept nodes:father and child of each one. Every concept can have n number ofchildren, but they only have one father. Thus, the relationships thatcan interact on that concept are expressed in the hierarchy too.Finally, application ontology with the properties, concepts thatcontain the domains and the hierarchy of each concept is generated(see Fig. 6).

On the other hand, let us describe the definitions for generatingthe concepts table (see Table 1) as follows.

For a concepts table, let ci,j be a concept that belongs to the set C,whereby a function father(ci,j) is proposed to return a concept cp,q,which is defined as the father of ci,j.

Thus, let ci,j be a concept related to the function child(ci,j) thatreturns the concept(s) cp,q, which is (are) child (children) of ci,j.Therefore, the function is defined as follows: child(ci,j)¼cp,q.

Fig. 4. Representation of the synthesis process.

Fig. 5. The mapping approach.


Let Pi,j be the set of properties that directly belongs to a conceptci,j, of a particular domain dijdi2D, which is defined byPi,j¼p(i,j,1),p(i,j,2),/,p(i,j,n).

According to the relationships, let Ri,j be a set of topologicalrelations that are associated to a concept ci,j of a particular domaindijdi2D, which is defined by Ri,j¼r(i,j,1),r(i,j,2),/,r(i,j,n).

By taking into account those definitions, the function exist_-concept receives a label eti and returns the identification number ofthe interest concept. Otherwise, if the concept does not exist, aBoolean value is returned (“false” in this case). The function isdefined as follows.

exist conceptðetiÞ ¼�

cj 0 � j � nfalse dof

In order to generate the concepts table, it is necessary to define

the function exist_synonymous, which receives a label and returnsthe number of the interest concepts or their relevancy. Otherwise, ifthe concept does not have any synonymous, the function returns aBoolean value (“false” in this case), when any concept has a syn-onymous. It is defined as follows.

exist synonymousðetiÞ ¼�

cj 0 � j � nfalse dof

3.1.3.2. The frequency table of concepts in the domains.According to the collected information of each domain previouslydefined, there is a set of concepts that belongs to a particulardomain. Thus, we can obtain the frequency of the concepts in thegeographic domains.

Therefore, let D be the set of domains, where d is a particular

Fig. 6. RAIN ontology obtained from the semantic assessment process.

Table 1The concepts table.

Conceptname

Synonyms Property Father Child Topologicalrelation

ci,1 Si,1 Pi,1 father(ci,1) child(ci,1) Ri,1ci,2 Si,2 Pi,2 father(ci,2) child(ci,2) Ri,2/ / / / / /

ci,n Si,n Pi,n father(ci,n) child(ci,n) Ri,n/ / / / / /

cm,n Sm,n Pm,n father(cm,n) child(cm,n) Rm,n


geographic domain that has been defined by the followingexpression: D¼d1,d2,…,dn. Now, let C be the set of domains, inwhich c is a concept involved in the geographic domain, defined byC¼c1,c2,…,cn.

By using the previous definitions, we are able to build theconcepts frequency table in the domains, which contains all thedomains that can be submitted in the ontology O, and also theconcepts located in each domain (see Table 2).

In order to simplify the notation of the concepts, we defined afunction that relates to a concept with the identification number ofthe domain, as well as the index of the concept at the same domain.The function concept receives two parameters, which describes thenumber of the domain and the number of the concept, returningthe number of the interest concepts. Otherwise, it returns a Boolean

Table 2The frequency table of concepts in the domains.

Domain Concepts

D1 C1 ¼ fcð1;1Þ; cð1;2Þ;/; cð1;n1ÞgD2 C1 ¼ fcð2;1Þ; cð2;2Þ;/; cð2;n2ÞgD3 C1 ¼ fcð3;1Þ; cð3;2Þ;/; cð3;n3Þg/ /

Dm C1 ¼ fcðm;1Þ; cðm;2Þ;/; cðm;nmÞg

value (“false”) when there is not any concept. The function conceptis defined as follows: concept(d,c)¼cj,kj0�j�m,0�k�n.

3.1.3.3. The synonyms domain table. This table allows us to knowthe possible alias that the particular domain could have and thedirect relationship with its search (see Table 3). Therefore, let Si bethe set of synonyms for a specific domain di, which is defined bySi¼{s(i,1),s(i,2),…,s(i,n)}.

3.1.3.4. The composition table of topological relations. In order tosemantically process the geospatial information, it is necessary toobtain the set of topological relations that are directly involvedbetween geographic objects in each domain for defining theirrelevance. The goal to process these relationships is based ondescribing the behavior or interaction of those objects, because thesemantics is implicitly defined in the topological relations (Kurata& Egenhofer, 2006; Budak Arpinar et al., 2006; Euzenat, Gomez-Perez, Guarino, & Stuckenschmidt, 2002). According to the above,the generation of a composition table of topological relations isproposed. This table is ordered, considering its relevance inside ofsome particular domain. The composition table is presented inTable 4.

Now, let rt be a relationship of the composition table, which isintegrated by the concepts ci and ci,cj2C and rt2R, denoted byrt¼ciricj.

Table 3The synonyms domain table.

Domain Concepts

D1 S1 ¼ fsð1;1Þ; sð1;2Þ;/; sð1;n1ÞgD2 S1 ¼ fsð2;1Þ; sð2;2Þ;/; sð2;n2ÞgD3 S1 ¼ fsð3;1Þ; sð3;2Þ;/; sð3;n3Þg/ /

Dm S1 ¼ fsðm;1Þ; sðm;2Þ;/; sðm;nmÞg

Table 5The semantic refinement table.

Input labels Output domains

E1¼{e11,e12,/,e1n} output1¼(D)E2¼{e21,e22,/,e2n} output2¼(D)E3¼{e31,e32,/,e3n} output3¼(D)/ /

Em¼{em1,em2,/,emn} outputm¼(D)

Table 4The composition table of topological relations.

Domain Relevance labels

Necessary Common Rare

Dt,1 NED1 COD1 RAD1

Dt,2 NED2 COD2 RAD2

Dt,3 NED3 COD3 RAD3

/ / / /

Dt,m NEDi CODi RADi


Let N be the set of necessary relationships presented in thegeographic domain i, where the presence of those relationships inthe domain indicates that they are always linked to interact in aparticular domain NDi¼{rtN1,rtN2,…,rtNn}.

Let C be a set a common relationships presented in thegeographic domain i, where the presence of those relationships inthe domain indicates that those concepts are commonly found in aparticular domain, such that CDi¼{rtC1,rtC2,…,rtCn}.

Let RA be a set of rare relationships presented in the geographicdomain. Their presence in the domain establishes that is unlikely tofind them in the domain. However, it is sometimes possible to findit out in very particular domains. Therefore, the set is defined asfollows: RADi¼{RtRA1,RtRA2,…,RtRAn}.

Fig. 7. Conceptual framewor

The domain of composition table Dti is composed of the union ofthe setsNDi, CODi and RADi, which is denoted byDti¼{NDi∪CODi∪RADi}.After obtaining the composition table, we proceed to rank the con-cepts and their topological relations, according to their relevance inthe domain. It points out that relationships of the set N are afundamental feature to define the domain. Thus, the common re-lationships are not fundamental features, because they could haveless relevance in the definition of the domain, such that it is not arequirement to count with those ones. Similarly, the relationships ofthe set RA, are not indispensable for defining the geographic domain;in addition, their relevance is below of the set C and it has also lessrelevance than the set N.

In consequence, the function relevant is defined. It receives atriplet that is composed of a pair of concepts and a geographicdomain. These items describe the number of domains and thenumber of the concepts, in the case of the triplet, it returns as resultthe relevance relationship of the triplet of our interest, which couldbe “necessary”, “common” or “rare”. The function is defined by thefollowing expression:

relevantðd; ca; cbÞ ¼�

true rtj ¼ fnecessary; common; raregfalse rtj ¼ ∅

3.1.3.5. The semantic refinement table. This table is defined to storethe labels that are received as the input of the method in order tovalidate the algorithms proposed in the inference stage. Thus, thelabels are assigned to a specific domain, after applying somequalitative spatial reasoning algorithms. This is done, when there isa validation performed by the user (see Table 5).

According to above, let return_ref be a function that receives setof input labels Ei¼{e11,e12,…,e1n}, which semantically describeeither one or more specific domains, returning as a result a set ofordered output domains, considering the closeness defined by thesemantic similarity with respect to the labels description defined

k of the inference stage.


by Exit(D). Therefore, the function is defined as follows:

return ref ðEiÞ ¼�

true ExitðDÞj0 � i � mfalse dof

3.2. The inference stage

The inference stage is composed of four tasks that interacttogether to analyze, describe and deduce which domain belongs toa set of geographic objects represented by labels. The first task

consists of establishing a mapping approach, which receives a set oflabels as an input. This set is used to search a concept defined in theontology and that is directly related to those labels. Later, conceptsthat have been mapped and related to the knowledge base in theontology are obtained. The second task consists of defining a set ofqualitative spatial reasoning approaches, which are determined bythree algorithms: (1) conceptual frequency, (2) relevance, and (3)semantic genealogy.

These algorithms carry out the inference process, considering asan input a set of concepts described in the ontology (knowledgebase). The third task is proposed to define a comparison of the al-gorithms, based on the results of applying each method accordingto the degree of effectiveness, which could change with the userinteraction.

Finally, the semantic refinement task consists of providing ananswer to the user, taking into account a validationprocess, inwhichthe feedback plays an important role to examine the semanticrichness of the representation. The obtained inference is stored inthe knowledge base to be part of the conceptualization and deter-mine the degree of effectiveness of the reasoning algorithm. In Fig. 7,a conceptual framework of inference stage is depicted.

3.2.1. The mapping approachIt is an algorithm designed to receive the input labels and

localize if there are concepts related to those labels in order toautomatically store or populate in the ontology as instances of aconcept class (synthesis process). However, it is necessary to verifyif there is a previous result for this set of labels, using the semanticrefinement table. A set of existing inputs inside the a prioriknowledge, or a set of ordered domains D is obtained with thisapproach. In case that labels have already been previously addedand assesed by the user, they will be stored as a part of theconceptualization in ontology O. The algorithm to perform themapping is presented in Algorithm 1.

3.2.2. The qualitative spatial reasoning approachesWe propose three algorithms in order to perform qualitative

spatial reasoning. The conceptual frequency approach is in chargedof counting the occurrences of each concept in a geographicdomain. The relevance approach searches the relationship that ex-ists between the concepts, which are received as input, and theirimportance in the geographic domain. The semantic genealogyapproach consists of obtaining the father concepts, computing thehierarchy of concepts that involves to a geographic object repre-sented by the domain.

3.2.2.1. The conceptual frequency algorithm. This algorithm consistsof counting the number of occurrences to compute the frequencythat each set of concepts appears in a particular domain. Thisprocess is called conceptual frequency.

In this algorithm the output is sorted from the highest to thelowest value, according to their repetitions. It receives conceptsthat have been previously verified by means of the mapping algo-rithm. This guarantees that the set of concepts is stored in theknowledge base.

Later, it is necessary to use the concepts frequency table in thedomains in order to search how many times each concept appearsin each geographic domain that contains the knowledge base. InAlgorithm 2, the conceptual frequency algorithm is presented.


3.2.2.2. The relevance algorithm. The relevance algorithm receivesthree parameters: a set of input concepts, in which if the conceptsexist, then they are obtained from the mapping approach, thesecond is a set of relevance composition table in the domain, andthe third is a mapping vector.

This algorithm is used to rank the importance degree of theconcepts in the domain. It provides the highest semantic richnessto the concepts in each particular domain. It also performs a searchof all the concepts that are received as input in the relevancecomposition table of each domain. The goal is to know if thoseconcepts are related with others. In Algorithm 3, the relevance al-gorithm is described for a set of concepts that represent geographicobjects.

3.2.2.3. The semantic genealogy algorithm. This algorithm isdivided into three tasks. The first is to search the father and chil-dren concepts of each one of the input concepts. The second task

consists of using the relevance algorithm in order to obtain thedomain. In this case, only the first result obtained by the relevancealgorithm will be considered. The last task performs a sum of theoutputs to show the domain that have appeared most with thegiven inputs into the relevance algorithm. The result of this algo-rithm is either a domain or an empty set, indicating that the domainhas not been found.

The process of the semantic genealogy algorithm is thefollowing: first, if the mapping vector VM is false, then it receivesthe input concepts. Consequently, the father class of each one of theinput n�concepts is searched. Later, it substitutes the i�th conceptby the father concept. The goal is to invoke the relevance algorithmwith the new set of labels. The obtained result from the relevance

algorithm is stored as the first element obtained in an outputvector, which contains the domain with the frequency that suchdomain is repeated. This process is iterative according to the

Fig. 8. Architecture of the RAIN system.

Fig. 9. Conceptual particular framework.


Fig. 10. Conceptual general framework.


number of father concepts that are found in the analysis. The pro-cedure for the children concepts of each input concept is similar,but the difference is that each input concept can have a m number

of children concepts, such that each son concept will be an indi-vidual input for the conceptual frequency algorithm. The semanticgenealogy algorithm is described in Algorithm 4.


4. Experimental results

This section presents the results of applying the RAIN method-ology. They are outlined by each stage defined in this work.

4.1. System architecture

The architecture of the system is depicted in Fig. 8. It iscomposed of three elements. The first is the repository where theconceptual frameworks are processed. The second is in charged ofloading the persistent model of database, which is built from theontology. The third is the input of the system that is directly relatedto the inference stage. It consists of querying information of thepersistent model in order to return the general concept to a certaindomain or geographic context.

4.2. Conceptual frameworks

In order to represent the knowledge, we propose conceptualframeworks as a basic structure, which are able to be readable by amachine. In this work, we have chosen the use of conceptualframeworks described in (Minsky, 1974, 1980). The implementation

Fig. 11. The persistent model gene

of these structures is based on XML meta-language (Zambon &Sekler, 2007), because according to its structure, it is possible tocarry out a hierarchical classification and organization of the apriori knowledge. The proposed conceptual frameworks are dividedinto two types: particular and general.

The conceptual particular framework (see Fig. 9) contains infor-mation of the concepts that directly integrate and represent aspecific geographic domain, with data that correspond to the name,synonyms, father and children concepts.

The conceptual general framework (see Fig. 10) is based on defi-nitions of a given domain by means of the topological relations,which exist between concepts that describe the domain and theirsynonyms. This type of framework defines a context for the con-cepts and synonyms that are used in the reasoning task.

4.3. Persistent model of the ontology-based design

The persistent model has been built using the RAIN ontology, inorder to store the translation of concepts, relationships and prop-erties, as well as the instances of these items into a repository. It iscomposed of nine tables that are designed to receive informationfrom the analysis and conceptualization stage by means of the

rated from the RAIN ontology.


conceptual frameworks.The description of tables that compose the persistent model,

shown in Fig.11 is the following: the concepts table, which containsinformation related to the name of the concept, location in thehierarchy (father and children). The synonyms table stores infor-mation about the known names of the concepts. The table ofproperties contains the characteristics of each concept. The

Fig. 12. The main hierarchy of cl

Fig. 13. The RAIN

composition table stores information related to topological re-lations that are presented between concepts, domain that theybelong to, and the level of relevance inside the domain (necessary,common and rare relationships). Finally the table of input labelscontains information of the labels that is received by the inferencestage.

As we have mentioned above, the model is built considering the

asses in the RAIN ontology.

application.


RAIN ontology (see Fig. 12). The RAIN ontology describes the defi-nition of concepts and topological relations that representgeographic objects and their behavior among them inside thegeographic domains. This ontology is also implemented accordingto the Kaab ontology and using the GEONTO-MET methodology forits building (Torres et al., 2011).

4.4. The RAIN application

The RAIN application is composed of four elements, which aredepicted in Fig. 13. The first element points out the input of thesystem to introduce the a priori knowledge, using the conceptualframeworks (see number “1”). The second element (see number“2”) is the input to add the set of labels in order to infer the domainthat labels belong to. In this section, the algorithms to apply qual-itative spatial reasoning and the method for comparison the resultsare located. The third element (see number “3”) shows the opera-tions that are performing over the repository. The forth element

Fig. 14. Results of the conceptual frequency algorithm.

Table 7The composition table of topological relations.

Table 6The table of concepts frequency.

Domain Frequency Output

River Delta 7 {river, lake, green area, land sea,body of water, island, sandy land}

Coast 3 {sea, sandy land, river}

(see number “4”) presents the results obtained by the RAIN appli-cation, depending on the selected algorithm.

Domain Concept Topological relation Concept Relevance

River Delta River Connect Sea NecessaryRiver Delta Island Share Sea CommonRiver Delta Sandy land Connect Sea RareCoast Sandy land Connect Sea NecessaryCoast River Cross Green area CommonCoast River Connect Sea Common

4.5. Test and results obtained by the qualitative spatial reasoningalgorithms

This test presents the results obtained by applying the concep-tual frequency algorithm, using the geographic domains river delta

and coast. First, we load the a priori knowledge to the repository ofthe RAIN application, using both conceptual frameworks (identifiedby number “1”). In Table 6, the frequency of each concept for thementioned domains is presented.

Therefore, the input labels used in the test are the follows: <sea,sandy land, river, island, green area>. The output obtained was<river delta>, because it was the domain with more occurrencesand in the second place the domainwas<coast>, with 3 concepts inthis domain. In Fig. 14, the result of conceptual frequency algorithmis depicted. We can appreciate the number of occurrences directlyfrom the ontology in each domain per concept.

However, this approach presents a problem that is directlyrelated to the domains. When the user introduces labels that arelocated in both domains (i.e., <sea, sandy land>), the same output isobtained. In order to solve the ambiguity, a distinction among thelabel is performed, taking into account the importance degree in-side the domain. Thus, the relevance algorithm is proposed to solvethe repetitions of occurences. It considers the definition of theconcepts according to their topological relations that are implicitlyinvolving them. The composition of topological relations is pre-sented in Table 7.

Now, it is possible to repeat the test when the userintroduces <sea, sandy land>. When the relevance algorithm isapplied, the first obtained domain is <coast>, followed by <riverdelta>. The fact is that definition of each one of the domains, bothconcepts exist, but only in <coast>, a necessary relationship is


presented, which is defined by “sandy land shares sea”, whereasthe relevance in the domain of “river delta is less”. It is unusual tofind this kind of relationship in that domain or context. In Fig. 15,the result of applying the relevance algorithm is shown.

On the other hand, when the user introduces concepts that arenot explicitly defined in the domains; for instance, let <perennial,sea> be input labels, where “perennial” belongs to subclass of“river”, the semantic genealogy algorithm is used in order to searchthe father of that concept and subsequently execute the relevancealgorithm for obtaining the result. Moreover, it is necessary tosearch the children classes and verify whether those definitionsexist. The final step consists of repeating this procedure for theconcept “sea”. In Fig. 16, the results of applying the semantic

Fig. 15. Results of the re

Fig. 16. Results of the semantic genealogy algorithm.

Table 8Comparison of the qualitative spatial reasoning algorithms.

Input labels Conceptual frequency

<Sea, sandy land> River delta, Coast<sea, sandy land, river, island, green area> River delta<River, sea> River delta, Coast<Perennial, sea> River delta, Coast<Composition, sea> River delta

genealogy algorithm is depicted.In Table 8, we present the summary with respect to the results

obtained from the three qualitative spatial algorithms. We canappreciate that the best result is generated by the relevant algo-rithm, because it has three correct answers with respect to the otheralgorithms. The reason is that it considers the topological relationsbetween the geographic concepts in order to infer the domain. Thesemantic genealogy algorithm produces acceptable inferences,because it establishes the neighborhood in the ontological hierar-chy of the concepts (father and children). The conceptual frequencyis the algorithm that presents problems, when some labels arelocated in both domains, because the occurrence of the conceptsdoes not determine in an adequate way the domain for a set of

levance algorithm.

labels. In Fig. 17, the process to compare and validate the results ofthe three algorithm is depicted.

5. Conclusion and future works

In this work, a methodology mainly composed of three ap-proaches to carry out an inference process is described. These ap-proaches are focused on performing qualitative spatial reasoninginto geographic objects descriptions.

Thus, a knowledge base is generated by means of applicationontology, which has been built in OWL, using the GEONTO-METmethodology. This conceptual structure represents the a priori

Relevance Semantic genealogy Correct inference

Coast No results CoastRiver delta Coast River deltaRiver delta No results River deltaNo results River delta River deltaNo results Coast Coast

Fig. 17. Comparison and validation process of the qualitative spatial algorithms.


knowledge of different geographic domains. Moreover, we proposethe use of conceptual frameworks to represent explicitly theknowledge of any domain, in order to structure and organize thesemantics of the geographic context. These frameworks describethe synonyms, names, relationships, properties and other charac-teristics related to geographic objects of any particular geographicdomain.

We argue that any qualitative spatial reasoning algorithm con-sists of two tasks: 1) a searching task and 2) a ranking task based onthe relevance of the characteristics or relationships. In addition, we

assert that a priori knowledge is a formal structure, which containsthe vocabulary, rules for the language and a set of logical proposi-tions that allow us to fundamentally solve problems associated toambiguity, uncertainty and vagueness of the geographic data.

The inference stage depends directly on particular data that arestored in the conceptual frameworks, which is denoted by a prioriknowledge. In fact, the qualitative spatial reasoning algorithms arecomplementary to each one. The best result is provided by therelevance approach, because it considers a priori knowledge such asthe topological relationships and properties defined in conceptual


frameworks. The semantic genealogy is iterative in order toconsider the execution of the conceptual frequency and relevanceapproaches. In the case that the knowledge is not defined in theconceptual framework, it would not be possible to infer about theconceptual structure for determining the concepts and theirinteraction in a particular domain.

Moreover, a definition of spatial reasoning is proposed. It con-sists of transforming a descriptive representation in another moregeneral, taking into account the semantics of the topological re-lationships. It is important to note that the process performed inthis work, attempts to generalize toward a superior class or conceptin an inverse sense to the semantic granularity that is defined by aconceptual representation, whereupon a machine can process thegeographic entities, in a similar way that we as human beingscognitively process and understand the real world in a generalizedmanner. This fact is implicitly related to compare the results ob-tained by our approach. According to the above, we consider thatthe best evaluation is performed by a domain expert, who has theknowledge to say if the inferred results are coherent and precise.

Future works are focusing on making more tests in differentgeographic domains as well as other totally different contexts. It isnecessary to compare the inferred results provided by our meth-odology with other semantic reasoners such as Pellet, DLog, OWL-DL, RacerPro, Cyc, FaCTþþ, etc., in order to evaluate different resultsand compare them, computing the same tests in such reasoners.Other work is oriented towards enriching the conceptual frame-works as well as the application ontology with more geometric,direction and mereological relationships for improving the infer-ence approaches, considering more semantic granularity togeneralize concepts and determine a specific domain.

Acknowledgments

This work was partially sponsored by the Instituto Polit�ecnicoNacional (IPN), Consejo Nacional de Ciencia y Tecnología (CON-ACYT) under grant 106692, and the Secretaría de Investigaci�on yPosgrado (SIP) under grants 20151176, 20151652, 20151408, and20151163. Additionally, we are thankful to the reviewers for theirinvaluable and constructive feedback that helped improve thequality of the paper.

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